Let$$s consider the pulley system placed on a rough incline. The system is initially stationary, and an external force P $=$P Ey is applied. The Block A has a mass of mA$,$ the Block B has a mass of mB$,$ and the pulleys are massless. The terms $$s and $$d are the coefficients of static and dynamic friction, respectively. Neglect the friction between the two blocks. A B P $$s$,$d Ex Ey $($a$)$ Starting with the position vectors, rA $=$ yAEy and rB $=$ yBEy $+$c$,$ define the kinematics of the problem $($c is a constant vector from A to B$).$ Show the kinematical relationships between Block A and Block B $($by analyzing the pulley system$).($b$)$ For each block, provide a free body diagram. Be careful with the gravitational force and provide a clear expression for the friction force. $($c$)$ Derive the equations of motion for each block. $($d$)$ Find the critical external force P$$ to move Block A$.$ Provide your answer as a function of mA$,$ mB$,$ g$,$ $,$ and $$s$.$